Preheat your oven to 350°F (175°C). This takes about 10-15 minutes. Place the oven rack in the middle position. Remove your pie crust from the refrigerator if frozen and place it in a 9-inch pie pan. The crust should be fully thawed or it may crack during baking.
In a large mixing bowl, combine 1 cup all-purpose flour and 1 cup granulated sugar. Whisk these dry ingredients together for about 1 minute until fully mixed with no lumps. Checkpoint: The mixture should look like fine sand.
Crack 4 large eggs directly into the flour-sugar mixture. Whisk vigorously for 2-3 minutes until the eggs are completely broken up and incorporated. The mixture should look pale and slightly foamy.
Add 1/2 cup fresh lemon juice (about 3-4 lemons) and 2 tablespoons lemon zest to the egg mixture. Whisk for 1-2 minutes until well combined. The filling will be bright yellow and fragrant.
Pour in 1/2 cup melted butter slowly while whisking constantly for about 1 minute. Add 1/4 teaspoon salt and whisk for another 30 seconds. Checkpoint: The mixture should be smooth, homogenous, and have no visible lumps.
Gradually add 1 cup whole milk to the filling, whisking slowly and steadily for 2-3 minutes until the filling is completely smooth and creamy. If you add the milk too quickly, lumps may form—if this happens, strain the filling through a fine-mesh sieve into a bowl and proceed.
Pour the entire filling mixture slowly and carefully into the unbaked pie crust, filling it to about 1/4 inch from the top. Do not pre-bake the crust. If filling spills over, use a paper towel to wipe the crust edges.
Carefully transfer the pie to the preheated 350°F oven on the middle rack. Bake for 40-45 minutes. The filling should be set and firm around the outer 2 inches of the pie, but the center (about a 2-inch circle in the middle) should still jiggle slightly when you gently shake the pan—this is exactly what you want. The surface should not brown or crack. Checkpoint: Insert a toothpick about 1 inch from the center; it should come out nearly clean or with just a few moist crumbs clinging to it.
Remove the pie from the oven using oven mitts. The filling will look custard-like and glossy. Place it on a wire cooling rack and allow it to sit at room temperature for 1 hour until it stops steaming. Do not move it around during this time.
Once cooled to room temperature, carefully transfer the pie to the refrigerator and chill for at least 2-3 hours (or overnight). As the pie chills, the filling will continue to set and firm up into a beautiful custard-like texture. Checkpoint: The pie is ready to serve when chilled and the filling no longer jiggles when the pan is gently shaken.
When ready to serve, remove the pie from the refrigerator and let it sit at room temperature for 5-10 minutes for easier slicing. Use a sharp, wet knife to cut clean slices, wiping the blade between each cut. If desired, dust each slice lightly with powdered sugar just before serving.
Store covered in the refrigerator (see Storage section for details). The pie stays fresh for up to 3 days.